Semiconductor Nanospheres and Quantum Dots

1
Semiconductor Nanospheres and Quantum Dots

• EE 150
• Joyce Poon
• May 1, 2003

2
Outline

• Introduction
• Some basic physics
• Fabrication methods
• Applications
• Lasers
• Optical nonlinearity
• Quantum optics
• Future outlook

3
Introduction

• Quantum dots (QD) a.k.a. quantum boxes and
  artificial atoms
• Discrete energy levels
• Focus on optical properties of quantum dots
• But interesting electronic transport properties
  also!
• Technological impact
• Interesting science

4
Some Basic Physics

• Density of states (DoS)
• e.g. in 3D

5
Discrete States

• Quantum confinement ? discrete states
• Energy levels from solutions to Schrodinger
  Equation
• Schrodinger equation
• For 1D infinite potential well
• If confinement in only 1D (x), in the other 2
  directions ? energy continuum

6
In 3D

• For 3D infinite potential boxes
• Simple treatment considered here
• Potential barrier is not an infinite box
• Spherical confinement, harmonic oscillator
  (quadratic) potential
• Only a single electron
• Multi-particle treatment
• Electrons and holes
• Effective mass mismatch at boundary (boundary
  conditions?)

7
Optical Excitation

• Exciton bound electron-hole pair (EHP)
• Excite semiconductor ? creation of EHP
• There is an attractive potential between electron
  and hole
• mh gt me ? hydrogenic syetem
• Binding energy determined from Bohr Theory
• In QDs, excitons generated inside the dot
• The excitons confined to the dot
• Degree of confinement determined by dot size
• Discrete energies
• Exciton absorption ? d function-like peaks in
  absorption

8
Size Matters

• Small enough to see quantum effect
• A free electron
• 3/2kBT ?2k2/2m
• l 60 ? at 300K
• For quantum effects 10s ?
• In semiconductors, use me (effective mass)
  instead
• me /me 1/10
• For quantum effects 100s ? (10s nm)
• Number of atoms 103 - 106
• Small L ? larger energy level separation
• Properties determined by size of QD

Energy levels must be sufficiently separated to
remain distinguishable under broadening (e.g.
thermal)
9
Fabrication Methods

• Goal to engineer potential energy barriers to
  confine electrons in 3 dimensions
• 3 primary methods
• Lithography
• Colloidal chemistry
• Epitaxy

10
Lithography

• Etch pillars in quantum well heterostructures
• Quantum well heterostructures give 1D confinement
• Mismatch of bandgaps ?? potential energy well
• Pillars provide confinement in the other 2
  dimensions
• Electron beam lithography
• Disadvantages Slow, contamination, low density,
  defect formation

A. Scherer and H.G. Craighead. Fabrication of
small laterally patterned multiple quantum wells.
Appl. Phys. Lett., Nov 1986.
11
Colloidal Particles

• Engineer reactions to precipitate quantum dots
  from solutions or a host material (e.g. polymer)
• In some cases, need to cap the surface so the
  dot remains chemically stable (i.e. bond other
  molecules on the surface)
• Can form core-shell structures
• Typically group II-VI materials (e.g. CdS, CdSe)
• Size variations ( size dispersion)

CdSe core with ZnS shell QDs
Red bigger dots! Blue smaller dots!
Evident Technologies http//www.evidenttech.com/p
roducts/core_shell_evidots/overview.php Sample
papers Steigerwald et al. Surface derivation
and isolation of semiconductor cluster molecules.
J. Am. Chem. Soc., 1988.
12
Epitaxy Patterned Growth

• Growth on patterned substrates
• Grow QDs in pyramid-shaped recesses
• Recesses formed by selective ion etching
• Disadvantage density of QDs limited by mask
  pattern

T. Fukui et al. GaAs tetrahedral quantum dot
structures fabricated using selective area metal
organic chemical vapor deposition. Appl. Phys.
Lett. May, 1991
13
Epitaxy Self-Organized Growth

• Self-organized QDs through epitaxial growth
  strains
• Stranski-Krastanov growth mode (use MBE, MOCVD)
• Islands formed on wetting layer due to lattice
  mismatch (size 10s nm)
• Disadvantage size and shape fluctuations,
  ordering
• Control island initiation
• Induce local strain, grow on dislocation, vary
  growth conditions, combine with patterning

• AFM images of islands epitaxiall grown on GaAs
  substrate.
• InAs islands randomly nucleate.
• Random distribution of InxGa1xAs ring-shaped
  islands.
• A 2D lattice of InAs islands on a GaAs substrate.

P. Petroff, A. Lorke, and A. Imamoglu.
Epitaxially self-assembled quantum dots. Physics
Today, May 2001.
14
QD Lasers

• Advantages
• More efficient, higher material gain, lower
  threshold
• Concentration of carriers near band edge
• Less thermal dependence, spectral broadening
• Material gain
• Theoretical prediction
• G104 cm-1, Jth5A/cm2 at RT
• Compared to bulk InGaAsP
• N1018, G102 cm-1

Ledenstov et al. Quantum-dot heterostructure
lasers. JSTQE, May 2000.
15
QD Heterostructure Lasers

• Stack QD vertically to increase density of QD
  (10 layers)
• Carrier escape at high T
• Higher modal gain (shape of mode x bulk gain)
• III-V based structures
• InAs-(In,Ga,Al)As ? near IR (1.83 mm) to red
• (In,Al)GaN-GaN? wide bandgap, can emit in the
  blue end of spectrum, even UV (with Al)

InGaAs QDs in AlGaAs (RT) Jth 60 A/cm2, Pout
3W CW InGaN QDs in GaN (RT) Jth 1 kA/cm2
N. Ledenstov et al. Quantum-dot heterostructure
lasers. JSTQE, May 2000. Y. Arakawa. Progress
in GaN-based quantum dots for optoelectronics
applications. JSTQE, July 2002.
16
Excitons and Nonlinear Optics

• Excitons enhance nonlinearity of materials at
  resonances
• Quantum confinement
• Discrete energy levels concentrate oscillator
  strength to lowest level transitions
• Oscillator Strength depends on
• Relative motion of the electron and hole
• Number of electron and hole pairs
• Larger dot
• Weak confinement, electron-hole more correlated,
  more nonlinearity
• Higher states have smaller fx, the oscillator
  strength eventually saturates

17
Nonlinear Optics
GaAs r 1.64x10-12 m/V

• InAs QDs and InGaAs QDs in GaAs
• 100x and 10x increase in electro-optic
  coefficient of pure GaAs
• Embed QDs (e.g. CdS, CdSe) in polymer (typically)
  host material to increase ?(3)
• Device applications optical switches, wavelength
  conversion

InAs r 2.438x10-10 m/V
InGaAs r 2.58x10-11 m/V
Ghosh et al. Nonlinear optical and electro-optic
properties of InAs/GaAs self-organized quantum
dots. J. Vac. Sci. Tech. B, 2001.

• Bulk PS linear
• Higher orders of nonlinearity present

n n0 (n2n4I)I
Du et al. Synthesis, characterization, and
nonlinear optical properties of hybridized
CdS-Polysterene nanocomposites. Chem. Mater.,
2002.
18
Quantum Optics

• Quantum mechanical system in solid-state!
• Cavity QED Modified spontaneous emission
• Spontaneous emission lifetime not intrinsic to
  atom but to coupling of atom vacuum
• Cavity modifies DoS of vacuum
• Couple QD to cavity
• Change in lifetime of spontaneous emission
• From 1.3 ns (no cavity) to 280 ps

Solid line PL spectrum Dashed line SE lifetime
QD in microcavity post
Solomon et al. Single-mode spontaneous emission
from a single quantum dot in a three-dimensional
microcavity, Phys Rev Lett, 2001.
19
Single Photon Sources

• Single photon emission through recombination of a
  single exciton
• Verified by studying g(2)(?), the 2nd order
  coherence function
• Observed photon-anti-bunching (quantum state of
  light)
• Optically pumped single photon source
• QDs in high Q microcavity at low T (5K)
• Lifetime of single exciton state shorter than
  lifetimes of the other states
• Electrically driven single photon source
• QDs in P-I-N junction
• At low current levels (10s of nA), low T (5K)
• Potential for quantum information processing,
  quantum computing

post Pelton et al. Efficient source of single
photons a single quantum dot in a micropost
microcavity. Phys Rev Lett., Dec. 2002. g(2) and
PIN Yuan et al. Electrically driven
single-photon source. Science, Jan. 2002. disk
Michler et al. A quantum dot single-photon
turnstile device. Science, Dec. 2000.
20
Future Outlook

• Development of QD lasers at communication
  wavelengths
• Gain and stimulated emission from QDs in polymers
• Polymeric optoelectronic devices?
• Probe fundamental physics
• Quantum computing schemes (exciton states as
  qubits)
• Basis for solid-state quantum computing?
• Biological applications
• Material engineering
• How to make QDs cheaply and easily with good
  control?
• Lets not forget the electronic applications too!
• Lots to do!

C. Seydel. Quantum dots get wet. Science, 300,
p. 80-81, Apr 2003.
21
Summary

• Discrete energy levels, artificial atom
• Fabrication top-down, bottom-up approaches
• Lithography, colloidal chemistry, epitaxy
• Making better lasers
• Enhancing optical nonlinear effects
• Quantum optics
• Lots of room for further research!

22
References

• Books
• Y. Masumoto and T. Takagahara. Semiconductor
  Quantum Dots Physics, Spectroscopy, and
  Applications. New York Springer-Verlag, 2002.
• P. Harrison. Quantum Wells, Wires, and Dots
  Theoretical and Computational Physics. New York
  Wiley, 2000.
• D. Dieter et al. Quantum Dot Heterostructures.
  New York Wiley, 1999.
• R.E. Hummel and P. Wibmann. Handbook of Optical
  Properties vol 2 Optics of Small Particles,
  Interfaces, and Surfaces. New York CRC Press,
  1995.
• General
• P. Petroff, A. Lorke, and A. Imamoglu.
  Epitaxially Self-Assembled Quantum Dots. Physics
  Today, May 2001.
• F. Julien and A. Alexandrou. Quantum Dots
  Controlling Artificial Atoms. Science 2825393.
• M. Reed. Quantum Dots. Scientific American, p
  118-123, Jan 1993.
• Fabrication
• T. Fukui et al. GaAs tetrahedral quantum dot
  structures fabricated using selective area metal
  organic chemical vapor deposition. Appl. Phys.
  Lett., 58(18), p. 2018-2020, 1991.
• Steigerwald et al. Surface derivation and
  isolation of semiconductor cluster molecules. J.
  Am. Chem. Soc., 110(10), p. 3046-3050, 1988.
• A. Scherer and H.G. Craighead. Fabrication of
  small laterally patterned multiple quantum wells.
  Appl. Phys. Lett., 49 (19), p. 1284-1286, 1986.

23
References (2)

• Lasers
• Y. Arakawa. Progress in GaN-based quantum dots
  for optoelectronics applications. JSTQE, 8(4),
  p. 823-832, 2002.
• N. Ledenstov et al. Quantum-dot heterostructure
  lasers. JSTQE, 6(3), p.439-451, 2000.
• V. Klimov. Optical gain and stimulated emission
  in nanocrystal quantum dots. Science, 290,
  p.314-317.
• L. Parvesl et al. Optical gain in silicon
  nanocrystals. Nature, 408, p.440-444, 2000.
• Optical nonlinearity
• Du et al. Synthesis, characterization, and
  nonlinear optical properties of hybridized
  CdS-Polysterene nanocomposites. Chem. Mater.,
  14, p. 4473-4479, 2002.
• Ghosh et al. Nonlinear optical and electro-optic
  properties of InAs/GaAs self-organized quantum
  dots. J. Vac. Sci. Tech. B, 19(4), p. 1071-1023,
  2001.
• R. E. Schwerzel et al. Nanocomposite photonic
  polymers. 1. Third-order nonlinear optical
  properties of capped cadmium sulfide nanocrystals
  in an ordered polydiacetylene host, J. Phys.
  Chem. A, 102, 5622-5626, 1998.
• Cavity QED and Single photon sources
• Pelton et al. Efficient source of single
  photons a single quantum dot in a micropost
  microcavity. Phys Rev Lett.,89(23), 233602,
  2002.
• Yuan et al. Electrically driven single-photon
  source. Science, 295, p. 102-105, 2002.
• Solomon et al. Single-mode spontaneous emission
  from a single quantum dot in a three-dimensional
  microcavity, Phys Rev Lett, 86(17), p. 3903-3906,
  2001.
• Michler et al. A quantum dot single-photon
  turnstile device. Science, 290, p.2282-2285,
  Dec. 2000
• A. Imamoglu et al. Quantum information
  processing using quantum dot spins and cavity
  QED. Phys Rev Lett., 83(20), p. 4204-4207, 1999.